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D.5 – Further cosmology (HL only)

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Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics) » D.5 – Further cosmology (HL only)

Description

Nature of science:

Cognitive bias: According to everybody’s expectations the rate of expansion of the universe should be slowing down because of gravity. The detailed results from the 1998 (and subsequent) observations on distant supernovae showed that the opposite was in fact true. The accelerated expansion of the universe, whereas experimentally verified, is still an unexplained phenomenon. (3.5)

Understandings:

The cosmological principle
Rotation curves and the mass of galaxies
Dark matter
Fluctuations in the CMB
The cosmological origin of redshift
Critical density
Dark energy

Applications and skills:

Describing the cosmological principle and its role in models of the universe
Describing rotation curves as evidence for dark matter
Deriving rotational velocity from Newtonian gravitation
Describing and interpreting the observed anisotropies in the CMB
Deriving critical density from Newtonian gravitation
Sketching and interpreting graphs showing the variation of the cosmic scale factor with time
Describing qualitatively the cosmic scale factor in models with and without dark energy

Guidance:

Students are expected to be able to refer to rotation curves as evidence for dark matter and must be aware of types of candidates for dark matter
Students must be familiar with the main results of COBE, WMAP and the Planck space observatory
Students are expected to demonstrate that the temperature of the universe varies with the cosmic scale factor as

Data booklet reference:

International-mindedness:

This is a highly collaborative field of research involving scientists from all over the world

Theory of knowledge:

Experimental facts show that the expansion of the universe is accelerating yet no one understands why. Is this an example of something that we will never know?

Aims:

Aim 2: unlike how it was just a few decades ago, the field of cosmology has now developed so much that cosmology has become a very exact science on the same level as the rest of physics
Aim 10: it is quite extraordinary that to settle the issue of the fate of the universe, cosmology, the physics of the very large, required the help of particle physics, the physics of the very small

Directly related questions

16N.3.HL.TZ0.25a:
Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is 5.0 × 10^–21 kg m^–3.
16N.3.HL.TZ0.25b: Explain why the rotation curves are evidence for the existence of dark matter.
17M.3.HL.TZ1.17a:
The graph shows the variation with time t of the cosmic scale factor R in the flat model of the universe in which dark energy is ignored.

On the axes above draw a graph to show the variation of R with time, when dark energy is present.
17M.3.HL.TZ1.17b.ii:
The density of dark energy is ρ_Λc² where ρ_Λ = ρ_c – ρ_m. Calculate the amount of dark energy in 1 m³ of space.
17M.3.HL.TZ2.20a:
Describe what is meant by dark matter.
17M.3.HL.TZ2.19a.ii:
The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100. Estimate the temperature of the CMB at the time of its emission.
17M.3.HL.TZ2.19b:
State how the anisotropies in the CMB distribution are interpreted.
17M.3.HL.TZ2.20c:
Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible stars in the galaxy.

Explain how curve A provides evidence for dark matter.
17M.3.HL.TZ1.17b.i:
The density of the observable matter in the universe is only 0.05 ρ_c. Suggest how the remaining 0.27 ρ_c is accounted for.
17M.3.HL.TZ2.19a.i:
Derive, using the concept of the cosmological origin of redshift, the relation

T $\propto \frac{1}{R}$

between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R.
17M.3.HL.TZ2.20b:
The distribution of mass in a spherical system is such that the density ρ varies with distance r from the centre as

ρ = $\frac{k}{{{r^2}}}$

where k is a constant.

Show that the rotation curve of this system is described by

v = constant.
20N.3.HL.TZ0.24b:
Identify two possible causes of the anisotropies in (a).
20N.3.HL.TZ0.21c: Hubble originally linked galactic redshift to a Doppler effect arising from galactic recession....
20N.3.HL.TZ0.24a: State the nature of the anisotropies observed in the CMB radiation.
17N.3.HL.TZ0.20c:
Show that the critical density of the universe is

$\frac{{3{H^2}}}{{8\pi G}}$

where H is the Hubble parameter and G is the gravitational constant.
17N.3.HL.TZ0.20b:
Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.
18M.3.HL.TZ1.19a:
The mass of visible matter in the galaxy is M.

Show that for stars where r > R₀ the velocity of orbit is v = $\sqrt {\frac{{GM}}{r}}$ .
18M.3.HL.TZ1.19c:
Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R₀.
18M.3.HL.TZ1.19b:
Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.
18M.3.HL.TZ2.19a:
Explain the evidence that indicates the location of dark matter in galaxies.
18M.3.HL.TZ2.19b:
Outline why a hypothesis of dark energy has been developed.
21N.1.SL.TZ0.30: Which is correct for a black-body radiator? A. The power it emits from a unit surface area...
18N.3.HL.TZ0.21b:
The present temperature of the cosmic microwave background (CMB) radiation is 3 K. Estimate the size of the universe relative to the present size of the universe when the temperature of the CMB was 300 K.
18N.3.HL.TZ0.20a: Outline what is meant by dark energy.
18N.3.HL.TZ0.20b: State two candidates for dark matter.
18N.3.HL.TZ0.21a:
Show that the temperature of the universe is inversely proportional to the cosmic scale factor.
19M.3.HL.TZ1.20a: Light from distant galaxies is redshifted. Explain the cosmological origin of this redshift.
19M.3.HL.TZ1.20b.ii:
Compare and contrast, the variation with time of the temperature of the cosmic background (CMB) radiation, for the two models from the present time onward.
19M.3.HL.TZ1.20b.i: Draw, on the axes, a graph to show the variation with time of the cosmic scale factor R for the...
19M.3.HL.TZ2.22b:
At critical density there is zero total energy. Show that the critical density of the universe is: ${{\text{r}}_c} = \frac{{3H_0^2}}{{8\pi G}}$ .
19M.3.HL.TZ2.22a:
Justify that the total energy of this particle is $E = \frac{1}{2}m{v^2} - \frac{4}{3}\pi G{\text{r}}{r^2}m$ .
19M.3.HL.TZ2.22c: The accepted value for the Hubble constant is 2.3 × 10−18 s−1. Estimate the critical density of...
19N.3.HL.TZ0.16b(iii): It is estimated that less than 20 % of the matter in the universe is observable. Discuss how...
19N.3.HL.TZ0.16b(i): State what is meant by the critical density.
19N.3.HL.TZ0.16b(ii):
Calculate the density of matter in the universe, using the Hubble constant 70 km s^–1Mpc^–1.

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DP Physics Questionbank

D.5 – Further cosmology (HL only)

Description

Directly related questions

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